The end is near 5 days of class left Final Exam Tuesday, May 11 th, 11-1 Decimals Ratio and Proportion Percents.

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Presentation transcript:

The end is near 5 days of class left Final Exam Tuesday, May 11 th, 11-1 Decimals Ratio and Proportion Percents

Decimals and place value

Without using a calculator: Find the decimal representation of each of the following fractions: 1/5¼1/3 2/53/102/7 1/94/253/100 5/95/77/8

Rational Numbers As fractions: As decimals:

Decimals as rational numbers Some decimal numbers are rational numbers: but some are not. A decimal is a rational number if it can be written as a fraction with integer numerator and denominator. Those are decimals that either terminate (end) or have a repeating block of digits. Repeating decimals: …; … Terminating decimals: 4.8; ; 0.75

Irrational numbers A number that is not rational is called irrational. A decimal like … is not rational because although there is a pattern, it does not repeat. It is an irrational number. Compare this to … It is rational because 556 repeats. It is a rational number.

Comparing Decimals When are decimals equal? 3.56 = But, ≠ To see why, examine the place values = = Think of units, rods, flats, and cubes.

Ways to compare decimals Write them as fractions and compare the fractions as we did in the last section. Use base-10 blocks. Use a number line. Line up the place values.

Exploration 5.16 Use the base 10 blocks to represent decimal numbers and justify your answers. Work on this together and turn in on Thursday.

Homework for Thursday Read pp (top) in the textbook Textbook problems pp # 2b,d; 5b,d,f; 8 Exploration 5.16

Rounding 3.784: round this to the nearest hundredth is between 3.78 and On the number line, which one is closer to? is half way in between

Adding and Subtracting Decimals Same idea as with fractions: the denominator (place values) must be common. So, is really like ones tenths hundredths = 5.55

Multiplying Decimals As with whole numbers and fractions, multiplication of decimals is best illustrated with the area model

Standard Algorithm for Multiplying Decimals Why do we do what we do? Multiply 2.1 × 1.3 Explain the algorithm.

Dividing decimals Standard algorithm—why do we do what we do? Divide: ÷ 1.2